Lamp B is rated 75cd if two lamps illuminate a screen equally from distance if lamp A is rated 75cd.
Illumination on a screen is inversely proportional to the square of the distance and directly proportional to the luminous intensity of the lamp
I_A/(d_A )^2 =I_B/(d_B )^2
I_A is the illumination of the first lamp (75cad)
I_B is the illumination of the second lamp
d_A is the distance between the screen and the first lamp
d_B is the distance between the screen and the second lamp
d_A=d_B=d
75/(d)^2 =I_2/(d)^2
cross multiply
75(d)^2=I_2 (d)^2
Divide through by (d)^2
(75(d)^2)/(d)^2 =(I_2 (d)^2)/(d)^2
75=I_2
Therefore, the rating of the second lamp is also 75cd
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